Super Hirota bilinear equations for the super modified BKP hierarchy by Huizhan Chen

“…In this paper, the super modified BKP (SmBKP) hierarchy is constructed from the perspective of the neutral free superfermions by using highest weight representations of the infinite-dimensional Lie superalgebra b∞|∞(g). Based upon this, the corresponding super Hirota bilinear identity of the SmBKP hierarchy is obtained by using the super Boson-Fermion correspondence of type B, and some specific examples of super Hirota bilinear equations are given. …”
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Perturbing AdS6 × w S 4: linearised equations and spin-2 spectrum by Achilleas Passias, Paul Richmond

“…The modes that saturate the bounds belong to short multiplets which we identify in the representation theory of the f4 $$ \mathfrak{f}(4) $$ symmetry superalgebra of the AdS6 × w S 4 solution.…”
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Unconventional SUSY and Conventional Physics: A Pedagogical Review by Pedro D. Alvarez, Lucas Delage, Mauricio Valenzuela, Jorge Zanelli

“…Here we argue that SUSY can be realized in a different way, connecting spacetime and internal bosonic symmetries, combining bosonic gauge fields and fermionic matter particles in a single gauge field, a Lie superalgebra-valued connection. In this <i>unconventional</i> representation, states do not come in SUSY pairs, avoiding the doubling of particles and fields and SUSY is not a fully off-shell invariance of the action. …”
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Component d = 6 Born-Infeld theory with N = (2, 0) → N = (1, 0) supersymmetry breaking by Nikolay Kozyrev

“…Much like the case of the N = 2, d = 4 Born-Infeld theory, proper irreducibility conditions of the multiplet are selected by the invariance with respect to the external automorphisms of the Poincaré superalgebra. They are found in the lowest nontrivial order in the auxiliary field. …”
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Cubic interactions for arbitrary spin N $$ \mathcal{N} $$ -extended massless supermultiplets in 4d flat space by R.R. Metsaev

“…Su- perspace realization of relativistic symmetries of the N $$ \mathcal{N} $$ -extended Poincaré superalgebra on space of interacting fields is also obtained.…”
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Warped AdS 2 and SU(1, 1|4) symmetry in Type IIB by David Corbino

“…The existence of the Lie superalgebra SU(1, 1|4) ⊂ PSU(2, 2|4), whose maximal bosonic subalgebra is SO(1, 2)⊕SO(6)⊕SO(2), motivates the search for half-BPS solutions with this isometry that are asymptotic to AdS 5 ×S 5. …”
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Scalar products of Bethe vectors in the models with gl(m|n) symmetry by A. Hutsalyuk, A. Liashyk, S.Z. Pakuliak, E. Ragoucy, N.A. Slavnov

“…We study scalar products of Bethe vectors in the models solvable by the nested algebraic Bethe ansatz and described by gl(m|n) superalgebra. Using coproduct properties of the Bethe vectors we obtain a sum formula for their scalar products. …”
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Operadores-escada generalizados para sistemas quânticos by Hugo de Oliveira Batael, Josimar Fernando da Silva, Alexandre Nogueira da Silva, Saiara Fabiana Menezes dos Santos, Elso Drigo Filho

“…A superálgebra vem sendo aplicada na resolução de diversos problemas quânticos. …”
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Three-dimensional Maxwellian extended Bargmann supergravity by Patrick Concha, Lucrezia Ravera, Evelyn Rodríguez

“…Abstract We present a novel three-dimensional non-relativistic Chern-Simons supergravity theory invariant under a Maxwellian extended Bargmann superalgebra. We first study the non-relativistic limits of the minimal and the N $$ \mathcal{N} $$ = 2 Maxwell superalgebras. …”
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Large-c superconformal torus blocks by Konstantin Alkalaev, Vladimir Belavin

“…Considering different contractions of the Neveu-Schwarz superalgebra related to the large central charge limit we explicitly calculate three superblocks, osp(1|2) global, light, and heavy-light superblocks, and show that they are related to each other. …”
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Asymptotic representations and q-oscillator solutions of the graded Yang–Baxter equation related to Baxter Q-operators by Zengo Tsuboi

“…We consider a class of asymptotic representations of the Borel subalgebra of the quantum affine superalgebra Uq(glˆ(M|N)). This is characterized by Drinfeld rational fractions. …”
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Infinite-dimensional R-matrices for the relativistic scattering of massless modes on AdS2 by Juan Miguel Nieto García, Roberto Ruiz, Alessandro Torrielli

“…We also prove that the R-matrices enjoy an infinite-dimensional symmetry superalgebra that embeds that of AdS2. Finally, we verify that the R-matrices are also invariant under crossing symmetry.…”
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The Dunkl-Cherednik deformation of a Howe duality by Ciubotaru, D, De Martino, M

“…For the second pair, we show that the classical copy of g ∼= spo(2|2, C) inside the Weyl-Clifford algebra W ⊗ C deforms to a Lie superalgebra inside Hc ⊗ C and compute its centraliser algebra. …”

Quantum SU(2|1) supersymmetric Calogero-Moser spinning systems by Sergey Fedoruk, Evgeny Ivanov, Olaf Lechtenfeld, Stepan Sidorov

“…In particular, we provide an N=4 $$ \mathcal{N}=4 $$ supersymmetrization of the quantum U(2) spin Calogero-Moser model, with an intrinsic mass parameter coming from the centrally-extended superalgebra su^2|1 $$ \widehat{su}\left(2\Big|1\right) $$. …”
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All basic quantizations of $$D=3$$ D = 3 , $$N=1$$ N = 1 Lorentz supersymmetry by V. N. Tolstoy

“…Abstract By the supersymmetrization of a simple algebraic technique proposed in Lukierski and Tolstoy (Eur Phys J C 77:226, 2017) we obtain the complete classification of all basic (nonisomorphic) quantum deformations for the orthosymplectic Lie superalgebra $$\mathfrak {osp}(1|2;{\mathbb {C}})$$ osp ( 1 | 2 ; C ) and its pseudoreal and real forms in terms of the classical r-matrices. …”
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Three-dimensional non-relativistic extended supergravity with cosmological constant by Patrick Concha, Lucrezia Ravera, Evelyn Rodríguez

“…Abstract In this paper, we present two novel non-relativistic superalgebras which correspond to supersymmetric extensions of the enlarged extended Bargmann algebra. …”
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Superselection of the weak hypercharge and the algebra of the Standard Model by Ivan Todorov

“…One thus modifies the Lie superalgebra generated by the Higgs field. Equating the normalizations of Φ in the lepton and the quark subalgebras we obtain a relation between the masses of the W boson and the Higgs that fits the experimental values within one percent accuracy.…”
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Three-dimensional Poincaré supergravity and N-extended supersymmetric BMS3 algebra by Ricardo Caroca, Patrick Concha, Octavio Fierro, Evelyn Rodríguez

“…We extend our procedure to their respective asymptotic symmetries and show that the N=(1,2,4) super-BMS3 appear as expansions of one Virasoro superalgebra. Interestingly, the N-extended super-BMS3 obtained here are not only centrally extended but also endowed with internal symmetry. …”
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Integrable lambda models and Chern-Simons theories by David M. Schmidtt

“…In particular, this means that the (classical) AdS 5 × S 5 lambda model can be understood as a double Chern-Simons theory defined on the Lie superalgebra p s u 2 , 2 | 4 $$ \mathfrak{p}\mathfrak{s}\mathfrak{u}\left(2,2\Big|4\right) $$ after a proper dependence of the spectral parameter is introduced. …”
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Classification of linearly compact simple Nambu-Poisson algebras by Cantarini, Nicoletta, Kac, Victor

“…We introduce the notion of a universal odd generalized Poisson superalgebra associated with an associative algebra A, by generalizing a construction made in the work of De Sole and Kac [Jpn. …”
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